2. (08.05 HC)

Help with those three please!!

Scilla [17]

Answer:

Part 1) Option A. The axis of symmetry is x=4

Part 2) Option C. minimum

Part 3) Option A. (4,-4)

Part 4) Option B. (2,0) and (6,0)

Step-by-step explanation:

we have

$f(x)=x^{2}-8x+12$

Part 1) What is the axis of symmetry of the parabola described by the equation above?

we know that

The equation above is a vertical parabola open upward

The axis of symmetry is the x-coordinate of the vertex

Find the vertex of the parabola (convert the equation in vertex form)

$f(x)-12=x^{2}-8x$

$f(x)-12+16=x^{2}-8x+16$

$f(x)+4=x^{2}-8x+16$

$f(x)+4=(x-4)^{2}$

$f(x)=(x-4)^{2}-4$ ----> equation in vertex form

The vertex of the parabola is (4,-4)

so

The axis of symmetry is x=4

Part 2) The vertex of the equation above is also

we know that

The equation above is a vertical parabola open upward

therefore

The vertex is a minimum

Part 3) What is the vertex of the parabola described by the equation above

we know that

The equation of the parabola into vertex form is equal to

$f(x)=(x-4)^{2}-4$

therefore

The vertex of the parabola is (4,-4)

Part 4) What are the x-intercepts of the parabola described by the equation above

we know that

The x-intercepts are the values of x when the value of y is equal to zero

so

$f(x)+4=(x-4)^{2}$

f)x)=0

so

$4=(x-4)^{2}$

take square root both sides

$(x-4)=(+/-)2$

$x=4(+/-)2$

$x=4(+)2=6$

$x=4(-)2=2$

therefore

The x-intercepts are

(2,0) and (6,0)

7 0

3 years ago

10. Write a word problem for this equation: n ($25) = $125

Andrei [34K]

Answer:

The word problem is "How many $25 are there in $125?"

Step-by-step explanation:

Given

$n(\$25) = \$125$

Required

Write a word problem for the expression

We start by solving the given equation

$n(\$25) = \$125$

Divide both sides by $25

$\frac{n(\$25)}{\$25} = \frac{\$125}{\$25}$

$n = \frac{\$125}{\$25}$

$n = 5$

This implies that there are 5, $25 in $125

Hence; The word problem is "How many $25 are there in $125?"

6 0

4 years ago

Draw a rectangular fraction model to explain your thinking. Then, write a multiplication sentence. A. 2 3 of = 3 5

myrzilka [38]

Answer:

$\frac{2}{3}\ of\ \frac{3}{5} = \frac{2}{5}$

Step-by-step explanation:

Given

$\frac{2}{3}\ of\ \frac{3}{5}$

Solving (a): Multiplication sentence

$\frac{2}{3}\ of\ \frac{3}{5}$

Rewrite of as *

$\frac{2}{3}\ of\ \frac{3}{5} = \frac{2}{3}\ *\ \frac{3}{5}$

Solve

$\frac{2}{3}\ of\ \frac{3}{5} = \frac{2}{5}$

Hence, the multiplication sentence is:

$\frac{2}{3}\ of\ \frac{3}{5} = \frac{2}{5}$

Solving (b): Rectangular fraction model

In (a) above, the result is 2/5

The fraction model will be represented as thus:

Draw a rectangle
Partition in to 5 equal parts (5 represents the denominator)
Shade 2 of the 5 partitions (2 represents the numerator)

See attachment for model

5 0

3 years ago

Can someone please help me

Ainat [17]

Answer:

20

Step-by-step explanation:

If the two triangles are similar, then corresponding sides must share a constant ratio. This means that:

$\dfrac{10}{6}=\dfrac{25}{15}=\dfrac{x}{12}$

Let's use the second ratio:

$\dfrac{25}{15}=\dfrac{x}{12}$

Multiply both sides by 12:

$\dfrac{25\cdot 12}{15}=x \\\\x=20$

Hope this helps!

5 0

3 years ago

Translate this phrase into an algebraic expression. 18 more than twice a number

Lostsunrise [7]

Answer:

y = 2x + 18

Step-by-step explanation:

7 0

3 years ago

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